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List of Statistics and Time Value of Money Questions for CFA Exam 1
Define simple random sampling.
Define and interpret sampling error.
Define a sampling distribution
Distinguish between simple random and stratified random sampling.
Distinguish between time-series and cross-sectional data.
State the central limit theorem and describe its importance.
Calculate and interpret the standard error of the sample mean.
Distinguish between a point estimate and a confidence interval estimate of a population parameter.
Identify and describe the desirable properties of an estimate.
Calculate and interpret a confidence interval for a population mean, given a normal distribution with a
known population variance.
Describe the properties of Student’s t-distribution.
Calculate and interpret a confidence interval for a population mean, given a normal distribution with an
unknown population variance.
Discuss the issues surrounding selection of the appropriate sample size.
Define and discuss data-snooping/data-mining bias.
Define and discuss sample selection bias, survivorship bias, look-ahead bias, and time-period bias.
Define a hypothesis and describe the steps of hypothesis testing.
Define and interpret the null hypothesis and alternative hypothesis.
Distinguish between one-tailed and two-tailed hypothesis tests.
Define and interpret a test statistic.
Define and interpret a significance level and explain how significance levels are used in hypothesis
testing.
Define and interpret a Type I and a Type II error.
Define the power of a test.
Define and interpret a decision rule.
Explain the relationship between confidence intervals and tests of significance.
Distinguish between a statistical decision and an economic decision.
Discuss the p-value approach to hypothesis testing.
Identify the test statistic and interpret the results for a hypothesis test about the population mean of a
normal distribution with (1) known or (2) unknown variance.
Explain the use of the z-test in relation to the central limit theorem.
Identify the test statistic and interpret the results for a hypothesis test about the equality of two population
means of two normally distributed populations based on independent samples.
Identify the test statistic and interpret the results for a hypothesis test about the mean difference for two
normal distributions (paired comparisons test).
Identify the test statistic and interpret the results for a hypothesis test about the variance of a normally
distributed population.
Identify the test statistic and interpret the results for a hypothesis test about the equality of the variances
of two normally distributed populations, based on two independent random samples.
Distinguish between parametric and nonparametric tests.
Define and interpret a scatter plot.
Define and calculate the covariance between two random variables.
Define and calculate, and interpret a correlation coefficient.
Describe how correlation analysis is used to measure the strength of a relationship between variables.
Formulate a test of the hypothesis that the population correlation coefficient equals zero and determine
whether the hypothesis is rejected at a given level of significance.
Define an outlier and explain how outliers can affect correlations.
Explain the nature of a spurious correlations.
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Differentiate between the dependent and independent variables in a linear regression.
Distinguish between the slope and the intercept terms in a regression equation.
List the assumptions underlying linear regression.
Define and calculate the standard error of the estimate.
Define and calculate the coefficient of determination.
Calculate a confidence interval for a regression coefficient.
Identify the test statistic and interpret the results for a hypothesis test about the population value of a
regression coefficient.
Interpret a regression coefficient.
Calculate a predicted value for the dependent variable, given an estimated regression model and a value
for the independent variable.
Calculate and interpret a confidence interval for the predicted value of a dependent variable.
Describe the use of analysis variance (ANOVA) in regression analysis.
Define and interpret an F-statistic.
Calculate the future value (FV) and present value (PV) of a single sum of money.
Calculate an unknown variable, given the other relevant variables, in single-sum problems.
Calculate the FV and PV of a regular annuity and an annuity due.
Calculate an unknown variable, given the other relevant variables, in annuity problems.
Show the equivalence between present value and discounted future value.
Calculate the PV of a perpetuity.
Calculate an unknown variable, given the other relevant variables, in perpetuity problems.
Calculate the FV and PV of a series of uneven cash flows.
Solve time value of money problems when compounding periods are other than annual.
Distinguish between the stated annual interest rate and the effective annual rate.
Calculate the effective annual rate, given the stated annual interest rate and the frequency of
compounding.
Draw a time line, specify a time index, and solve problems involving the time value of money as applied
to mortgages, credit card loans, and saving for college tuition or retirement.
Differentiate between a population and a sample.
Explain the concept of a parameter.
Explain the differences among the types of measurement scales.
Define and interpret a frequency distribution.
Define, calculate, and interpret a holding period return.
Define and explain the use of intervals to summarize data.
Calculate relative frequencies, given a frequency distribution.
Describe the properties of data presented as a histogram or a frequency polygon.
Define, calculate, and interpret measures of central tendency, including the population mean, sample
mean, arithmetic mean, geometric mean, weighted mean , median mean, and mode.
Distinguish between arithmetic and geometric means.
Describe and interpret quartiles, quintiles, deciles, and percentiles.
Define, calculate, and interpret (1) a portfolio return as a weighted mean, (2) a weighted average or mean,
(3) a range and mean absolute deviation, and (4) a sample and a population variance and standard
deviation.
Calculate the proportion of items falling within a specified number of standard deviations of the mean,
using Chebyshev’s inequality.
Define, calculate, and interpret the coefficient of variation.
Define, calculate, and interpret the Sharpe measure of risk-adjusted performance.
Describe the relative locations of the mean, median, and mode for a nonsymmetrical distribution.
Define and interpret skewness and explain why a distribution might be positively or negatively skewed.
Define and interpret kurtosis and explain why a distribution might have positive excess kurtosis.
Describe and interpret measures of skewness and kurtosis.
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Explain why a semi-logarithmic scale is often used for return performance graphs.
Define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events.
Explain the two defining properties of probability.
Distinguish among empirical, a priori, and subjective probabilities.
Describe the investment consequences of probabilities that are inconsistent.
Distinguish between unconditional and conditional probabilities.
Define a joint probability.
Calculate, using the multiplication rule, the joint probability of two events.
Calculate, using the addition rule, the probability that at least one of two events will occur.
Distinguish between dependent and independent events.
Calculate a joint probability of any number of independent events.
Calculate, using the total probability rule, an unconditional probability.
Define, calculate, and interpret expected value, variance, and standard deviation.
Explain the use of conditional expectation in investment applications.
Calculate an expected value using the total probability rule.
Define, calculate, and interpret covariance and correlation.
Explain the relationship among covariance, standard deviation, and correlation.
Calculate the expected return and the variance for return on a portfolio.
Calculate covariance given a joint probability function.
Calculate an updated probability, using Bayes’ formula.
Calculate the number of ways a specified number of tasks can be performed using the multiplication rule
of counting.
Solve counting problems using the factorial, combination, and permutation notations.
Distinguish between problems for which different counting methods are appropriate.
Calculate the number of ways to choose r objects from a total of n objects, when the order in which the r
objects is listed does or does not matter.
Explain a probability distribution.
Distinguish between and give examples of discrete and continuous random variables.
Describe the range of possible outcomes of a specified random variable.
Define a probability function and state whether a given function satisfies the conditions for a probability
function.
State the two key properties of a probability function.
Define a cumulative distribution function and calculate probabilities for a random variable, given a
cumulative distribution function.
Define a probability density function.
Define a discrete uniform random variable and calculate probabilities, given a discrete uniform
probability distribution.
Define a binomial random variable and calculate probabilities, given a binomial probability distribution.
Calculate the expected value and variance of a binomial random variable.
Construct a binomial tree to describe stock price movement and calculate the expected terminal stock
price.
Describe the continuous uniform distribution and calculate probabilities, given a continuous uniform
probability distribution.
Explain the key properties of the normal distribution.
Define the standard normal distribution and explain how to standardize a random variable.
Calculate probabilities using the standard normal probability distribution.
Distinguish between a univariate and a multivariate distribution.
Explain the role of correlation in the multivariate normal distribution.
Define shortfall risk.
Calculate the safety-first ratio and select an optimal portfolio using Roy’s safety-first criterion.
Explain the relationship between the lognormal and normal distributions.
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Distinguish between discretely and continuously compounded rates of return.
Calculate a continuously compounded return, given a specific holding period return.
Explain Monte Carlo simulation and historical simulation and describe their major applications and
limitations.
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